Based on the box-and-whisker plot shown below, match each term with the correct value.



(1)Median
a0
(2)Range
a1
(3)25th percentile
a2
(4)75th percentile
a3
(5)Inter-quartile Range
a4

The time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.

What is the unitary method ?

The unitary method is a method in which you find the value of one unit and then the value of required no. of units.

It is given that room is painted that has wall space of 400 feet². The time taken to paint this space is 2 and half hours.

So , the wall space painted per hour will be :

= 400 ÷ [tex]2\frac{1}{2}[/tex]

= 400 ÷ [tex]\frac{5}{2}[/tex]

= 400 × [tex]\frac{2}{5}[/tex]

= 160 square feet per hour

We have to find out the time taken to paint a room which has a wall space of 720 feet². So , this will be calculated by dividing 720 square feet wall space by the per hour painted wall space that is equal to:

= 720 / 160

= 4.5 hours

or

= [tex]4\frac{1}{2}[/tex] hours

Therefore , the time taken to paint a room which has a wall space of 720 feet² is equal to [tex]4\frac{1}{2}[/tex] hours.

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The width of the rectangle is 6 centimeters and the length is 19 centimeters.

To find the dimensions of the rectangle, we can assign variables to the length and width of the rectangle. Let's say the width is 'w' centimeters.

Therefore, the dimensions of the rectangle are width = 6 centimeters and length = 19 centimeters.

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x and y are the center point so since C and D are multiplied by x an y they would remain the same

E = the center points squared plus the radius squared.

 Since the radius is getting smaller E would also decrease

Answer is E

The quadratic equation[tex]x^2 + 14x + 49 = 0[/tex]factors into [tex](x + 7)^2 = 0[/tex], yielding one real repeated solution, x = -7. This means the graph of the quadratic function touches the x-axis at precisely one point.

The given equation [tex]x^2 + 14x + 49 = 0[/tex] is a quadratic equation and can be factored or solved using the quadratic formula.

However, this particular equation is a perfect square trinomial because the constant term 49 is the square of 7 and twice the product of 7 and the linear coefficient 14 is equal to the middle term 14x.

[tex]x^2+2*7*x+7^2=0[/tex]

Therefore, the equation can be factored as

(x + 7)^2 = 0.

To find the solution, we set the factor equal to zero:

(x + 7) = 0
(x + 7) = 0

This equation has one unique solution, x = -7, which means the quadratic equation has one real repeated solution.

In the context of the number and type of solutions, it means the graph of the quadratic function touches the x-axis at one point (x = -7) and does not cross it.

Answer:

A. |x| < 3

Step-by-step explanation:

The absolute value of a number is the value that a number has beyond its sign. This means that the absolute value is the numerical magnitude of the number regardless of whether its sign is positive or negative. Formally, the absolute value of any real number x, is defined by:

[tex]|x|=\left \{ {{x,\hspace{3}if\hspace{3}x\geq0} \atop {-x,\hspace{3}if\hspace{3}x<0}} \right.[/tex]

In this sense, to satisfy the inequality [tex]|x|<3[/tex], the domain of x must be:

[tex]-3<x<3\\\\or\\\\(-3,3)[/tex]

Because for [tex]x<-3[/tex] or [tex]x>3[/tex] the inequality is absurd. For example if x=-4

[tex]|-4|=4<3[/tex] which is not true.

and for x=4

[tex]|4|=4<3[/tex] which is not true.

On the other hand  to satisfy the inequality [tex]|x|>3[/tex], the domain of x must be:

[tex]-3>x>3\\\\or\\\\(-\infty,-3)\cup(3,\infty)[/tex]

Because for [tex]x<3[/tex]  the inequality is absurd. For example if [tex]x=2[/tex]

[tex]|2|=2>3[/tex] which is not true.

and for x=-1

[tex]|-1|=1>3[/tex] which is not true.

Therefore the correct statement is:

A. |x| < 3

Buying an asset or a vehicle means paying off the entire sum of money that is the cost of the asset at the time of its purchase.

Leasing an asset means purchasing an asset by not paying the entire sum of money at the time of purchasing, rather paying in the form of rent over the period of time.

If a person wants to purchase his dream car for keeping for many years, then Buying Option is better because the payment of the overall cost in buying will be less than leasing.

This will also provide benefit that at the time of sale the owner will be paid off higher value of car as compared to car taken on lease.

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If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Buying a car provides long-term ownership, customization options, and potential resale value, while leasing offers lower monthly payments but no ownership.

If a person wants to purchase their dream car and keep it for many years, it is generally recommended to buy rather than lease. Here are the reasons why:

In conclusion, buying a car is a better option if you want long-term ownership and the ability to customize the vehicle. Leasing may be suitable for those who prefer lower monthly payments and don't want to commit to long-term ownership.

The total distance that he drive is:

                     110 miles.

We know that the distance is defined as the product of speed and time.

i.e.

[tex]Distance=Speed\times Time[/tex]

It is given that:

Juan drives 50 mph for 1.5 hours.

This means that at this rate the distance traveled by him is:

[tex]Distance_1=50\times 1.5\\\\i.e.\\\\Distance_1=75\ miles[/tex]

and he travels at the rate of 70 mph for 0.5 hours.

This means that the distance traveled by him at this rate is:

[tex]Distance_1=70\times 0.5\\\\i.e.\\\\Distance_1=35\ miles[/tex]

Hence, the total distance that he drive is:

      [tex]Total\ distance=Distance_1+Distance_2\\\\Total\ distance=75+35\\\\i.e.\\\\Total\ distance=110\ miles[/tex]

The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66.

A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

Given two points,

(12, 10) , (-2, r)

The slope associated with (x₁, y₁) and (x₂, y₂) →

Slope(m) = (y₂ - y₁)/(x₂ - x₁)

So,

m = (r - 10)/(-2-12)

(r - 10)/(-14) = -4

r - 10 = 56

r = 66

Hence "The value of r such that the slope associated with two points (12, 10), (-2, r) is -4 is 66".

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2620 /4 = 655 per week

 suppose you work 40 hours per week

655/40 = $16.38 per hour

that is a good pay, but training all depends on the actual job.

 some jobs don't require any training, some require 3 months or more.

 it also depends on your education

1km = 1000 m

22*1000 = 22,000

 Answer is D. 22,000

Final answer:

The most important variable to determine the top wind speed at 4:00 p.m. is B. the miles-per-hour speed of the wind at its maximum point. The calculation shows an initial speed of 20 mph at 9:00 a.m., with an increase of 3 mph each hour leading to a top speed of 41 mph at 4:00 p.m.

Explanation:

The variable most important to the problem of determining the top wind speed recorded is B. the miles-per-hour speed of the wind at its maximum point. To find the top speed, you can calculate the increase in wind speed from the initial measurement at 9:00 a.m. The wind was increasing by 3 miles per hour each hour until it reached its peak at 4:00 p.m.

Here is the calculation:    

Top wind speed = Initial speed + (Increase per hour × Number of hours)
Top wind speed = 20 mph + (3 mph/hour × 7 hours)
Top wind speed = 20 mph + 21 mph
Top wind speed = 41 mph

Answer:

-147

Step-by-step explanation:

1km = 0.621371 miles

 so equation  is

total miles per hour = 11.5km * 0.621371

Final answer:

To solve 12 cot2(x) = 4, we simplify and use properties of the tangent function. The solution is x = π/3, 2π/3, 4π/3, and 5π/3 within the interval [0, 2π].

Explanation:

To solve the trigonometric equation 12 cot2(x) = 4, we first simplify it to find cot2(x) = 1/3 by dividing both sides by 12. To find cot(x), we take the square root of both sides, giving us cot(x) = ±1/√3. Remember that cot(x) is the reciprocal of tan(x), so we now have tan(x) = ±√3.

To find the values of x that satisfy this equation within the interval [0, 2π], we look at the unit circle. The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. Therefore, for tan(x) = √3, x = π/3, 4π/3, and for tan(x) = -√3, x = 2π/3, 5π/3. These are the values of x in the given interval that satisfy the equation.